n = 1150
x = 114
p = x/n
p = 114/1150 = 0.099
z critical value = ____
(Then, I got this formula from the question in the 'Related Questions' below. I hope this helps.)
E = za/2 *sqrt((p (1-p)/)/n))
Create a 90% confidence interval for the percentage of people the company contacts who may buy something.
x = 114
p = x/n
p = 114/1150 = 0.099
z critical value = ____
(Then, I got this formula from the question in the 'Related Questions' below. I hope this helps.)
E = za/2 *sqrt((p (1-p)/)/n))
Confidence Interval = Sample Proportion ± (Critical Value) * (Standard Error)
First, let's calculate the sample proportion (p̂) using the number of orders received (114) and the sample size (1150):
p̂ = Number of orders / Sample Size = 114 / 1150 = 0.0991
Next, we need to determine the critical value, which depends on the level of confidence desired. For a 90% confidence level, we need to find the z-score corresponding to a confidence level of 0.90. Consulting a z-table, we find that the z-score for a 90% confidence level is approximately 1.645.
Now, we need to calculate the standard error (SE) using the sample proportion:
SE = sqrt((p̂ * (1 - p̂)) / n)
SE = sqrt((0.0991 * (1 - 0.0991)) / 1150) ≈ 0.0091
Finally, we can calculate the confidence interval by plugging in the values:
Confidence Interval = 0.0991 ± (1.645 * 0.0091)
Confidence Interval = 0.0991 ± 0.015
The 90% confidence interval for the percentage of people who may buy something is approximately 0.0841 to 0.1141, or 8.41% to 11.41%.
Confidence Interval = Sample Proportion ± (Z * √((Sample Proportion * (1 - Sample Proportion)) / Sample Size))
In this case, the sample proportion is the number of people who bought something divided by the sample size. Let's calculate the confidence interval step-by-step:
Step 1: Calculate the sample proportion
Sample Proportion = Number of people who bought something / Sample size
Sample Proportion = 114 / 1150
Sample Proportion ≈ 0.0991
Step 2: Find the Z-value for a 90% confidence interval
Since we want a 90% confidence interval, we need to find the Z-value for a 95% confidence level (1 - (1 - 0.90) / 2 = 0.95).
Using a standard normal distribution table or calculator, the Z-value for a 95% confidence level is approximately 1.645.
Step 3: Calculate the standard error
Standard Error = √((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
Standard Error = √((0.0991 * (1 - 0.0991)) / 1150)
Standard Error ≈ 0.00934
Step 4: Calculate the margin of error
Margin of Error = Z * Standard Error
Margin of Error = 1.645 * 0.00934
Margin of Error ≈ 0.01532
Step 5: Calculate the lower and upper bounds of the confidence interval
Lower Bound = Sample Proportion - Margin of Error
Lower Bound = 0.0991 - 0.01532
Lower Bound ≈ 0.0838
Upper Bound = Sample Proportion + Margin of Error
Upper Bound = 0.0991 + 0.01532
Upper Bound ≈ 0.1144
Therefore, the 90% confidence interval for the percentage of people the company contacts who may buy something is approximately 8.38% to 11.44%.